We assign a Gaussian process prior \(\Pi \)  on the regression function \(f \sim \mathrm {GP}(0, \sigma ^2 (n \lambda )^{-1} K)\) , where \(K(\cdot ,\cdot ):\mathcal {X}\times \mathcal {X}\rightarrow \mathbb {R}\)  is a continuous, symmetric and positive definite bivariate function (i.e., the Mercer kernel), and \(\lambda >0\)  is a regularization parameter that possibly depends on the sample size \(n\) . The rescaling factor \((n\lambda )^{-1}\)  in the covariance kernel connects Bayes estimator with the kernel ridge regression [1]}, [2]}; see also [3]} and Theorem 11.61 in [4]} for more discussion on this connection.
